Three-way switches are the ones operated by more than one switch, such as the ones you would have at the top and bottom of stairs to operate a light. A common service call we get is when these switches are improperly wired.
Symptoms of improper wiring include the system only working from one switch and not the other, or a certain switch needing to be in one position for any of the others to work. Fixing this problem is usually a minimal service charge.
If you attempt to correct this problem yourself, it is extremely important that you turn off the power to the switches first! A professional will not always do this, but only because they know which wires bite and which ones don't. DO NOT attempt to mimic the work habits of a professional, this can be VERY dangerous—even deadly.
When in doubt, call a professional, licensed electrician. Your safety is worth far more than a service call.